江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目:Ergodic theory under nonlinear expectations
报告人：赵怀忠 教授 英国杜伦大学
报告时间：2025年12月23日（周二） 9：00-10：00
报告地点：数学学院B301
报告摘要:
In this talk, I will discuss the ideas of ergodic theory of a dynamical system under the nonlinear expectation space/nonadditive probabilities. Ergodicity is defined as that any invariant set or its complement has upper probability 0, we call the (0,0)-regime (Feng-Zhao (SIMA 2021)). It was proved that the ergodicity is equivalent to the irreducibility of the measurable dynamical systems, the eigenvalue 1 of the Koopman operator being simple, Birkhoff’s law of large numbers with single value. For a stochastic system under a sublinear Markov setup, the theory was also developed via lifting to canonical dynamical systems. It is proved that the G-Brownian motion on the unit circle is ergodic. Following this initial work, many progresses have been made recently. One work is Zhao-Zhao (Preprint 2025) on the existence of invariant expectations of G-SDEs. Another work is Feng-Huang-Liu-Zhao (AAP 2026 and Preprint 2024) on the equivalence of the (0,0)-regime with the ergodicity of invariant skeleton measure, and mixing. I will also discuss a weaker regime that any invariant set has upper probability 0 or 1 of Cerreia-Vioglio, Maccheroni and Marinacci (2016). We call this (0,1)-regime. We proved that the weak (0,1)-regime does not give the irreducibility, but is equivalent to a decomposition of finite (0,0)-regime ergodic components.
报告人简介：
赵怀忠教授 1984 年毕业于山东大学数学系数学专业，1990 年在中国科学院应用数学所获得博士学位（动力系统)，1995 年取得英国华威大学数学研究所博士学位（随机分析）。先后在中科院应用数学研究所、英国华威大学数学研究所、意大利国际理论物理中心（ICTP）、英国斯旺西大学、美国加利福尼亚大学尔湾分校任职，曾任两届拉夫堡大学数学院院长，现
为英国杜伦大学讲席教授，山东大学高层次人才特聘教授。曾入选英国工程 与 物 理 科 学 基 金 委 资 深 人 才 计 划 （ EPSRC Established Career Fellowship)、上海市海外高层次人才、国家海外高层次人才。在 Mem. Amer. Math. Soc.、Comm. Math. Phys.、J. Funct. Anal.、J. Differ. Equ.、Ann. Appl. Probab.等期刊上发表论文 70 余篇。主要研究方向为随机分析，涉及随机微分方程/随机偏微分方程、非线性期望特别是随机动力系统理论、遍历性理论等。